Listen to Robert Emmerich introduce The Big Apple, a hit song from 1937. Music written by Bob and performed by Tommy Dorsey's Clambake Seven with Bob on piano. Lyrics written by Buddy Bernier and sung by Edythe Wright. Audio provided by Dorothy Emmerich.

Max, it seems, has a new waiter, obviously of Chinese origin. A customer sat down at this particular waiter’s table and studied the menu. The waiter patiently hung around for several minutes and then bent over the man’s shoulder and said:

“Nu?”

THE CUSTOMER raised his eyebrows and ordered a pastrami on rye. The waiter—Chinese, mind you!—repeated the order to the chef, but spoke it in Yiddish.

“SHHH,” cautioned Max, “not so loud. He just came over to this country and he thinks he’s learning English!”

15 September 1957, Boston (MA) Advertiser, “The Wit Parade” by E. E. Kenyon, The American Weekly, pg. 18, col. 2:
The current story around Manhattan is about a middle-west rabbi who was visiting New York and was taken to dinner at a famous Jewish restaurant on the east side of town.

As he gave his order in Yiddish he looked up amazed to find it being taken by a Chinese waiter.

“Extraordinary!” he said to the proprietor later. “Where did you ever find a Chinese waiter who speaks Yiddish?”

The proprietor quickly put a finger to his lips.

“Sh-h-h,” he said, “he really thinks he’s learning English.”

Google News Archive
21 April 1961, The Dispatch (Lexington, NC), “Try and Stop Me” by Bennett Cerf, pg. 4, col. 6:
A RABBI VISITED his favorite Jewish restaurant, and was astounded when a Chinese waiter came to take his order. Furthermore, the Chinese waiter spoke Yiddish! When he left in the direction of the kitchen, the rabbi summoned the proprietor, and said, “Where on earth did you ever find a Chinese waiter who can speak Yiddish?”

Google BooksThe Cambridge Companion to Philip Roth
Edited by Timothy Parrish
Cambridge: Cambridge University Press
2007
Pg. 136:
Smilesberger’s ethnic joke concerns a Chinese waiter working in a Yiddish deli. A customer comes into the deli and is startled to find that his waiter is a Yiddish-speaking Chinese immigrant. Later, when paying for his meal, the customer raves to the owner of the deli about not only the terrific meal but also the Chinese waiter who speaks perfect Yiddish. ”Shah, shhh,” the owner replies with the joke’s punch line, “not so loud—he thinks he’s learning English.”

Google BooksPastrami on Rye:
An Overstuffed History of the Jewish Deli
By Ted Merwin
New York, NY: NYU University Press
2015
Pg. 161:
A couple goes out to eat one evening at the neighborhood kosher deli. They are amazed when a suave Chinese waiter, speaking perfect Yiddish, comes up to their table to take their order. On their way out, they ask the owner how he ever managed to train a Chinese waiter to speak Yiddish. “Shhh,” he tells them, “he thinks I;m teaching him English!”